Square shares surged by as much as 60% at the company's public trading debut on Thursday.
The shares closed up about 45%, at $13.07.
The mobile-payments company's stock opened at $11.20. Shares had been indicated to open at a range of $10.50 to $11.50, above the $9 pricing disclosed on Wednesday.
After the market close on Thursday, Square had a market cap of about $4.2 billion.
The indicated price had given the company a valuation of nearly $3 billion, half of where it was priced at its most recent private-financing round.
At that time, it raised $150 million at $15.50 per share.
It was already a bumpy start to the company's public debut. Still, it was one of the biggest public offerings of the year and will be closely watched as private tech startup valuations continue to soar.
It's not common for tech companies to price their IPOs below their worth at the preceding private-funding round.
Some analysts have suggested the lowered valuation happened, in part, out of concern about CEO Jack Dorsey, who returned to the helm of Twitter in October.
Square is trading on the New York Stock Exchange with the ticker SQ.
Here's a chart of the stock's first day:
